Theorem 1lt7

Description: 1 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	1lt7	$$⊢1<7$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		2lt7	$$⊢2<7$$
3		1re	$$⊢1\in ℝ$$
4		2re	$$⊢2\in ℝ$$
5		7re	$$⊢7\in ℝ$$
6	3 4 5	lttri	$$⊢\left(1<2\wedge 2<7\right)\to 1<7$$
7	1 2 6	mp2an	$$⊢1<7$$